WASHINGTON -LRB- CNN -RRB- -- President Obama affirmed his support for a woman 's `` right to choose '' on Thursday , the 36th anniversary of the Supreme Court decision that led to the legalization of abortion , as thousands of anti-abortion activists descended on the National Mall to challenge his position .

President Obama issued a statement defending Roe v. Wade for protecting `` women 's health and reproductive freedom . ''

Roe v. Wade `` not only protects women 's health and reproductive freedom , but stands for a broader principle : that government should not intrude on our most private family matters , '' Obama said in a statement .

The landmark 1973 decision held that a woman 's right to abortion was protected by the right to privacy under the Constitution 's 14th Amendment , voiding most state laws against abortion at the time .

Nellie Gray , who helped organize the anti-abortion March for Life on the Mall , invited Obama to speak at the rally .

`` America needs your strong leadership as president of all the people to stop the intentional killing of an estimated 3,000 pre-born boys and girls each day and the brutalizing of mind , heart and body of pregnant mothers . ''

Kim Gandy , president of the National Organization for Women , said she believes that while abortion should remain an option , increasing the availability and affordability of birth control and reducing the number of unwanted pregnancies is the real solution .

`` I think what everyone ought to be interested in doing , whether they are or not , is reducing the number of unwanted pregnancies , '' Gandy told CNN . `` Because if we reduce the number of unwanted pregnancies , it will by definition reduce the number of abortions and reduce a lot of the pain and despair that has befallen women in these economic times , who can not afford to enlarge their families when they do n't have a job and they do n't have a way to put food on the table for the kids that they have now .

`` If we could all work together to reduce the number of unwanted pregnancies , it would dramatically change the debate on this issue . ''

Obama has so far not struck down rules reinstated by the Bush administration eight years ago , prohibiting U.S. money from funding international family planning groups that promote abortion or provide information , counseling or referrals about abortion services .

The `` Mexico City policy '' was initially put in place by President Ronald Reagan and suspended during Bill Clinton 's presidency . Its opponents refer to it as the `` global gag order . ''

About 20 anti-abortion rights lawmakers spoke at the rally Thursday , pushing for a renewed effort to overturn Roe v. Wade .

`` At what instant does life begin ? '' asked Rep. Steve King , R-Iowa , focusing on younger crowd members who answered , `` Conception ! ''

`` And the next question is , '' he continued , `` President Obama , when did your life begin ? ''

Other legislators detailed their plans to keep the issue on the table in Congress and on the minds of voters .

Rep. Jean Schmidt , R-Ohio , told the crowd she plans to introduce what she calls the `` Juno Bill , '' referencing the hit 2008 film of the same title in which a high school teenager gives her baby up for adoption .

`` It will provide a tax credit to those women , just as we allow abortions to be tax deductible , it will provide a tax credit so that they can carry out their pregnancy , give that baby to a loving arm and not have to worry about the consequences or the costs involved , '' she said .

Throughout the rally , speakers urged bold action for their cause .

Gandy said the fight will also continue on the pro-abortion rights side .

`` There 's no question we have a pro-choice president now , but he ca n't do it alone , '' she said . `` He ca n't pass legislation . He ca n't stop what 's going on at the state and local level and so the battle rages on ... at the congressional level , at the state and local level and certainly at the Supreme Court . ''

She said the number of unwanted pregnancies is rising , as congressional action has increased the cost of contraception for college students and low-income women , `` something we hope this administration will reverse . ''

Two pieces of federal legislation are pending , she said . The first will expand accessibility and availability of birth control , and the second , the Freedom of Choice Act , is a codification of Roe v. Wade . NOW will continue pursuing both at the congressional level , she said , but noted that even though Congress has a Democratic majority , it does not have a pro-abortion rights majority .

`` So that will continue to be an uphill battle , '' she said

CNN 's Paul Courson and Mary Grace Lucas contributed to this report .

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Obama : `` Government should not intrude on our most private family matters ''

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Obama released statement on Roe anniversary while protesters descended on Mall

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Rally organizer to Obama : Stop intentional killing '' of unborn babies

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Former President Bush typically spoke by phone to rally each year